A number of processes and additives have been prepared and used to make textile fibers, and products produced therefrom, flame-retardant or noninflammable. However, often such additives or treatments result in fibers which present toxicity problems on use or which form toxic materials, such as gases, when exposed to heat or open flames. In addition, some additives are quite expensive or are required in such high concentrations to be effective that their use affects the fiber properties and become expensive at such concentration levels. It is, therefore, most desirable to provide textile fibers, particularly fibers composed of olefinic resins and similar polymers, with nonflammable properties at low cost, with low concentrations of additives and without the disadvantages of prior-art materials.